Models of non-abelian orbifolds

Several models of non-abelian orbifolds have been constructed. There are models with three or four families of quarks and leptons, and gauge symmetry SU(3) × SU(2) × SU(2) × U(1)² × SU(3)′ × SO(10)′ × U(1)′ or SU(3) × SU(2) × U(1)³ × SU(4)′ × SO(8)′ × U(1)′.     

A supersymmetric left-right confining model of the weak interactions

We extend the supersymmetric, confining theory of weak interactions to a left-right symmetric model. This model is based on the gauge group SU(M)_SC×SU(2)_R×SU(2)_L×SU(3)_c×U(1) and is more natural as far as supersymmetry breaking is concerned. Supersymmetry protects chiral symmetries from spontaneous breakdown and allows a solution to the strong CP problem. This model can accommodate at most three generations of quarks and leptons.     

A dynamical theory for the rishon model

We propose a composite model for quarks and leptons based on an exact SU(3)_C × SU(3)_H gauge theory and two fundamental $\text{J=}\text{1}\text{2}$ fermions: a charged T-rishon and a neutral V-rishon. Quarks, leptons and W-bosons are SU(3)_H-singlet composites of rishons. A dynamically broken effective SU(3)_C × SU(2)_L × SU(2)_R × U(1)_B?L gauge theory emerges at the composite level. The theory is “natural”, anomaly free, has no fundamental scalar particles, and describes at least three generations of quarks and leptons.     

Parity violating neutral currents in a left-right symmetric gauge model

We consider parity violating effects in the neutral sector of a left-right symmetric SU(2)_L × SU(2)_R × U(1) gauge model of weak and electromagnetic interaction. With four quarks and four leptons, the parity violating optical rotation in atoms is estimated to be about an order of magnitude smaller (and of opposite sign) compared to the Salam-Weinberg (SW) model prediction. However, with new quarks and leptons this effect can be arranged to be even smaller. Weak-electromagnetic interference effects are quantitatively different from those found in the SW model. A unified gauge theory which embeds the left-right symmetric gauge model is briefly discussed.     

Quasi nambu-goldstone fermions

We explore in detail the hypothesis that quarks and leptons are the approximately massless quasi Goldstone fermions of a supersymmetric preon theory. In particular, we discuss the possible patterns of states emerging from the spontaneous breakdown of global symmetries in supersymmetric theories and construct the low-energy effective lagrangians describing the interaction of these states. In contrast to what happens in the Goldstone sector, the interactions of the quasi Goldstone fermions contain arbitrary parameters which directly reflect the preon dynamics. Various models are explored, including both models in which the weak interactions are residual and models where these interactions are fundamental. A variety of issues are addressed, from the universality and approximate SU(2)_L nature of the weak interactions, for the former class of models, to the generation of states beyond the quarks and leptons and the nature of the dynamical breaking of SU(2)_L×U(1), for the latter class of models. Open questions and speculations connected with the origin of families and the nature of fermion mass generation, including supersymmetry breaking, are also discussed.     

Weak interactions of quasi nambu-goldstone fermions

We investigate the hypothesis that the observed weak interactions are the residual interactions of quasi Goldstone fermions. Left-handed quarks and leptons arise from the spontaneous symmetry breaking U(6) → U(4) × SU(2) in a supersymmetric theory. The simplest preon model realizing this breakdown leads, in the complementary picture, to the supersymmetric extension of the standard model of electroweak interactions. Furthermore, 't Hooft's anomaly conditions are satisfied with respect to the unbroken subgroup of the U(6) flavour symmetry and R-invariance. The preon model predicts the existence of a ninth chiral supermultiplet, the novino.     

Weak interactions as manifestations of the substructure of leptons and quarks

A new model for the substructure of leptons, quarks and weak bosons is investigated. The weak interactions are residual effects due to the substructure. No spontaneous symmetry breaking is needed to generate masses. The structure of the weak interactions at high energies is expected to deviate substantially from the one predicted by the standard SU(2) × U(1) theory.     

Unification of families based on a coset space E7/SU(5) × SU(3) × U(1)

We show that the usual three families of quarks and leptons are identifiable with quasi Nambu-Goldstone fermions in a supersymmetric non-linear realization of E₇ corresponding to the Kähler manifold E₇/SU(5) × SU(3) × U(1). So the triplication of families suggests the underlying preon theory realizing the global E₇ linearly. Possible connections with N = 8 supergravity are also discussed.     

Parity violations in hydrogen and the fundamental structure of the weak current

Experiments in progress with hydrogen and deuterium may in practice determine the fundamental parameters and constituents of the weak interaction within the framework of unified gauge theories. In particular, for SU (2) × U (1) theories, from the results of these experiments one can infer the masses of the charged and neutral weak vector bosons (and thus sin²θ_W), and the isospin classification of the right-handed portions of the electron and the u- and d-quarks. Non-singlet assignments for e_R, u_R and d_R would imply the existence of additional leptons and/or quarks. Hydrogen/deuterium data also may be used to discriminate between SU (2) × U (1) models and various models based on larger gauge groups.     

Trimuons in SU(3) gauge models

We discuss models of weak interactions which can account for the recently observed μ^?μ^?μ⁺ events in v_μ reactions by allowing for the production of a new heavy neutral lepton and a new quark. One model is based on an SU(3) × U(1) gauge theory in shich the left-handed leptons are classified in anti-triplets. The second model catagorizes the leptons in an octet in accord with the more restrictive SU(3) weak gauge theory.     

Quarks and leptons

We review the physics of quarks and leptons within the framework of gauge theories for the weak and electromagnetic interactions. The Weinberg-Salam SU(2) × U(1) theory is used as a “reference point” but models based on larger gauge groups, especially SU(2)_L × SU(2)_R × U(1), are discussed. We distinguish among thre “generations” of fundamental fermions: The first generation (e^?, ν_e, u, d), the second generation (μ^?, ν_μ, c, s) and the third generation (τ^?, ν_τ, t, b). For each generation we discuss the classification of all fermions, the charged and neutral weak currents, possible right-handed currents, parity and CP-violation, fermion masses and Cabibbo-like angles and related problems. We review theoretical ideas as well as experimental evidence, emphasizing open theoretical problems and possible experimental tests. The possibility of unifying the weak, electromagnetic and strong interactions in a grand unification scheme is reviewed. The problems and their possible solutions are presented, generation by generation, but a brief subject-index (following the table of contents) enables the interested reader to follow any specific topic throughout the three generations.     

Four families of composite quarks and leptons

Four families of composite quarks and leptons, two standard and two non-standard, are found in a unique solution SU(3)_HC × SU(6)_L × SU(6)_R of a restricted 't Hooft anomaly-matching program. Testable predictions emerge, such as prohibition of μ → eγ, zero charge asymmetry in e⁺e^? → τ⁺τ^? in contrast to e⁺e^? → μ⁺μ^?, and a rich new hadron spectrum masses around M_W. A minimal set of spectator fermions contains color-singlet objects with fractional quark-like charges.     

Cosmological constant in a model with superstring-inspired E 6 unification and shadow θ-particles

We have developed the concept of parallel existence of the ordinary (O-) and mirror (M-), or shadow (Sh-) worlds. In the first part of the paper we consider a mirror world with broken mirror parity and the breaking E ₆→SU(3)³ in both worlds. We show that in this case the evolutions of coupling constants in the O- and M-worlds are not identical, having different parameters for similar evolutions. E ₆ unification, inspired by superstring theory, restores the broken mirror parity at the scale ～10¹⁸ GeV. With the aim to explain the tiny cosmological constant, in the second part we consider the breakings: E ₆→SO(10)×U(1) _Z in the O-world, and E′₆→SU(6)′×SU(2)′ _θ in the Sh-world. We assume the existence of shadow θ-particles and the low-energy symmetry group SU(3)′ _C ×SU(2)′ _L ×SU(2)′ _θ ×U(1)′ _Y in the shadow world, instead of the Standard Model. The additional non-Abelian SU(2)′ _θ group with massless gauge fields, “thetons”, has a macroscopic confinement radius 1/Λ′ _θ . The assumption that Λ′ _θ ≈2.3?10^?3 eV explains the tiny cosmological constant given by recent astrophysical measurements. In this way the present work opens the possibility to specify a grand unification group, such as E ₆, from cosmology.     

Supersymmetric preon models with three-fermion generations

A class of supersymmetric preon models is considered in which the hypercolour groupG _HC and the unbroken flavour groupG _f anomalies are zero without needing spectators. It is shown that forG _HC=SU(2) and SU(3) quarks and leptons as composites can be obtained satisfying ’t Hooft’s anomaly matching conditions. For the case ofG _HC=SU(3),G _f can accommodate a horizontal symmetry group to describe just three generations.     

SU(3) × U(1) × U(1)′ gauge model of weak and electromagnetic interactions

An SU(3) × U(1) × U(1)′ gauge model of weak and electromagnetic interactions is proposed which satisfies the $\text{ΔT =}\text{1}\text{2}$ rule for non-leptonic decays of strange particles. The value of neutral leptonic currents predicted in the model agrees with the experimental data.     

Bounds on the number and masses of quarks and leptons

We assume weak, electromagnetic and strong interactions to be asymptotically divergent, and to become strong at very large energies, of the order of the Plank mass. In this picture, the “low-energy” couplings (i.e. in the 10² GeV region) must be near the infrared stable point, and this allows us to put bounds on the number of elementary fermions (quarks and leptons). Similar assumptions on the Higgs couplings give bound on the fermion and on the Higgs boson masses. We consider the cases where weak and electromagnetic interactions are described by the gauge groups SU(2) ? U(1) or SU(2)_R ? U(1). The weak neutral current mixing angle is computed in both cases.     

Supersymmetric extension of the SU(3)×SU(2)×U(1) model

We describe a class of supersymmetric SU(3)×SU(2)×U(1) models where all quarks and leptons, as well as their scalar partners, get masses through one-loop radiative corrections.     

Spontaneous breaking of global baryon number symmetry

We study the possibility that theU(1) _B global symmetry associated with baryon number is spontaneously broken. We present realistic examples implemented in the context of a suitably extended standardSU(2) _L×U(1)×SU(3)_c model and of a composite model of quarks and leptons. The globalU(1) _B symmetry in both cases is spontaneously broken at a relatively low mass scale without any conflict with observations. The dominant baryon number nonconserving process in these models obeys the ΔB=2 selection rule.     

High-colour and mass hierarchies

We present a model based on the gauge group G = G_HC × G_S × SU(2)_L × U(1), where the hypercolour gauge group G_HC is responsible for the dynamical breaking of the strong group G_S to SU(3)_C of QCD. Chiral symmetry breaking of high-colour representations produces dynamical breaking of the electroweak SU(2)_L × U(1) gauge group. Fermion masses and flavour mixing are dynamically generated from the condensations of high-colour representations. A phenomenological analysis of the model is also presented.     

Grand unified model with a stable proton and no axion problem

We present a grand unified model of the strong, electromagnetic and weak interactions based on a local SU(8)_L×SU(8)_R gauge theory which possesses a global U(8)_L × U(8)_R invariance. We break the symmetry down to the standard SU(3)_C × SU(2)_L × U(1) model, with the proton remaining stable and the left-handed neutrinos obliged to remain massless. A novel feature of our model is the simultaneous absence of both strong CP violations and of axions.